Magic Numbers and Optical Absorption Spectrum in Vertically Coupled Quantum Dots in the Fractional Quantum Hall Regime

TL;DR

This paper investigates the quantum states and optical absorption spectra of vertically coupled quantum dots in strong magnetic fields, revealing new correlation-induced magic numbers and their experimental signatures.

Contribution

It introduces a new sequence of angular momentum magic numbers arising from electron correlations in double quantum dots and discusses their experimental detection via optical absorption spectra.

Findings

Discovery of a new sequence of angular momentum magic numbers due to electron correlation.

Identification of discontinuities in absorption energy at magic number transitions.

Demonstration that optical spectra can reveal inter-dot electron tunneling effects.

Abstract

Exact diagonalization is used to study the quantum states of vertically coupled quantum dots in strong magnetic fields. We find a new sequence of angular momentum magic numbers which are a consequence of the electron correlation in the double dot. The new sequence occurs at low angular momenta and changes into the single dot sequence at a critical angular momentum determined by the strength of the inter-dot electron tunneling. We also propose that the magic numbers can be investigated experimentally in vertically coupled dots. Because of the generalized Kohn theorem, the far-infrared optical absorption spectrum of a single dot is unaffected by correlation but the theorem does not hold for two vertically coupled dots which have different confining potentials. We show that the absorption energy of the double dot should exhibit discontinuities at the magnetic fields where the total angular momentum changes from one magic number to another.